In this talk we discuss infinite-dimensional versions of well-known stability notions relating the external input u and the state x of a linear system governed by the equation x˙=Ax+Bu,x(0)=x0​. Here, A and B are unbounded operators. For instance, the system is called \textit{Lp-input-to-state stable} if u(⋅)↦x(t) is bounded as a mapping from Lp(0,t) to the state space X for all t3˘e0. In particular, we elaborate on the relation of this notion to \textit{integral input-to-state} stability and \textit{(zero-class) admissibility} with a special focus on the case p=∞.\\ This is joint work with B.~Jacob, R.~Nabiullin and J.R.~Partington